Exploring Hierarchies Using the DAGMap - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 100

Fig. 7.1 ( a ) Traditional Sugiyama node-link layout. ( b ) Corresponding DAGMap view of a DAG.
The node size and color correspond to node attributes such as the companies' assets and the
location of headquarters (color figure online)
by each of its parent companies. Image (a) in Fig. 7.1 a shows a part of a DAG
describing links between companies and their subsidiaries. The node (and link) color
and map size correspond to different attributes that can be computed from the DAG
(see Sect. 7.3 ).
Natural questions emerge when studying data modeled by DAGs. The level of
a node v in the DAG roughly corresponds to how “general” the node is. More
precisely, the level can correspond to how much of the DAG the node spans, or
how many nodes can be accessed going downwards from v . For companies, the
node level corresponds to the degree to which a company controls its subsidiaries
(and subsidiaries of its subsidiaries, etc.). This is even more the case when one
takes into account edge or node attributes, such as a company's assets. In our
case, the DAG structure also reveals the extent to which two (or more) companies'
strategies or interests overlap over a set of subsidiaries. We have developed a
technique that combines a node-link view with the DAG, explicitly showing links
between companies and visually indicating where a company is located in the whole
hierarchy. However, this type of view is not optimal for showing and comparing
node attributes. We have thus designed a DAGMap view, which constructs a
TreeMap ( Shneiderman , 1992 ) from a DAG, in order to emphasize node attributes,
such as the total capital of a company, making it easy to compare companies based
on attributes. Color coding semantic attributes, such as the country (or region) for
the company's headquarters, has been shown to be efficient in helping geographers
study how companies build strategies to avoid taxes, compete or collaborate with
others. For instance, the DAGMap view facilitates identifying small subsidiaries as
“tax havens”, while the node-link view helps clarify how small subsidiaries link to
ancestor companies or other subsidiaries.
The remainder of the chapter is organized as follows. We first present related
work, followed by a description of our case study, motivating the use of the